What is expand-(2x(-2x+6)^3)/(81) ?

The solution to expand-(2x(-2x+6)^3)/(81) is (16x^4}{81}-\frac{16x^3)/9+(16x^2)/3-(16x)/3

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expand-(2x(-2x+6)^3)/(81)

expand

- \frac{2 x ( - 2 x + 6 ) ^{3}}{81}

\frac{16 x ^{4}}{81} - \frac{16 x ^{3}}{9} + \frac{16 x ^{2}}{3} - \frac{16 x}{3}

Solution steps

- \frac{2 x ( - 2 x + 6 ) ^{3}}{81}

(- 2 x + 6)^{3} = - 8 x^{3} + 72 x^{2} - 216 x + 216

= - \frac{2 x ( - 8 x ^{3} + 72 x ^{2} - 216 x + 216 )}{81}

Expand

2 x (- 8 x^{3} + 72 x^{2} - 216 x + 216) : - 16 x^{4} + 144 x^{3} - 432 x^{2} + 432 x

= - \frac{- 16 x ^{4} + 144 x ^{3} - 432 x ^{2} + 432 x}{81}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- 16 x ^{4} + 144 x ^{3} - 432 x ^{2} + 432 x}{81} = - (- \frac{16 x ^{4}}{81}) - (\frac{144 x ^{3}}{81}) - (- \frac{432 x ^{2}}{81}) - (\frac{432 x}{81})

= - (- \frac{16 x ^{4}}{81}) - (\frac{144 x ^{3}}{81}) - (- \frac{432 x ^{2}}{81}) - (\frac{432 x}{81})

Remove parentheses:

(a) = a, - (- a) = a

= \frac{16 x ^{4}}{81} - \frac{144 x ^{3}}{81} + \frac{432 x ^{2}}{81} - \frac{432 x}{81}

Cancel

\frac{144 x ^{3}}{81} : \frac{16 x ^{3}}{9}

= \frac{16 x ^{4}}{81} - \frac{16 x ^{3}}{9} + \frac{432 x ^{2}}{81} - \frac{432 x}{81}

Cancel

\frac{432 x ^{2}}{81} : \frac{16 x ^{2}}{3}

= \frac{16 x ^{4}}{81} - \frac{16 x ^{3}}{9} + \frac{16 x ^{2}}{3} - \frac{432 x}{81}

Cancel

\frac{432 x}{81} : \frac{16 x}{3}

= \frac{16 x ^{4}}{81} - \frac{16 x ^{3}}{9} + \frac{16 x ^{2}}{3} - \frac{16 x}{3}

(4 t + 1) H (t - 1)

5 sin (\frac{π}{2} (x + 7)) - 8

2 (5 x + 2 y = - 6)

2940 T (z - e^{- T}) (z - e^{- 2 T}) (z - e^{- 7 T})

l im x \Rightarrow 5 (x + 7) 3 (3 x - 3)

What is expand-(2x(-2x+6)^3)/(81) ?
The solution to expand-(2x(-2x+6)^3)/(81) is (16x^4}{81}-\frac{16x^3)/9+(16x^2)/3-(16x)/3